Grade 12 math help please!! For what value of b will the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1?

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Grade 12 math help please!! For what value of b will the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1?

Mathematics
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okay I will show you:
thank you so much!
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thinking
oh ok sorry
sorry, it too late for me I will hand this over to lonesome else?
ok
thanks anyways
Here it goes~ Have you learnt remainder theorem yet?
@pottersheep Are you there??
Yes sorry, we have!
So, let R be the remainder when p(x) is divided by x-2. By remainder theorem, what would you get? I mean p(_) = ...?
ok one sec
So i'd sub in 2 for x
Yup!
3?
sorryryyryryryr
Sorry what do I do with the b though?
4b -24
Right, so for p(2), you get p(2) = 4b - 24 = R, agree? (By remainder theorem, p(a) = R , when p(x) is divided by x-a)
Right, okay
And what is the remainder when p(x) is divided by x+1 ?
b - 5
Not really.. Remainder = p(-1) = -2(-1)^3 + b(-1)^2 - 5(-1) +2 = ...?
Opps, sorry! I subbed in 1!
9??
b + 9!
Yes. Note that the remainder is p(x) = R when p(x) is divided by x-a. Now, p(x) is divided by x+1, so a = -1 in the case. [ x-(-1) = x+1]
True, sorry!
From the question, the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1. So, equate the two remainder you got and solve b. Got it?
Oh.. It's okay!
Ohhhhhhhhh, so make them equal to each other?? Yes I get it, thank you!!!!!!
Yes. Since they have the SAME remainder! You're welcome :)

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